Abstract There is much evidence that increasing temperatures due to climate change are having negative effects on yields of key staple crops, including wheat. In France particularly, a link has been shown between the stagnating wheat yields and an increase in heat stress occurrence during grain filling. We studied the occurrence of heat stress during grain filling of wheat under climate change by coupling downscaled weather scenarios from the ARPEGE climate model with a modified version of the ARCWHEAT phenology model. We also explored the effects of different agronomic solutions: earlier sowing, use of earlier cultivars and improved genetic tolerance to heat stress. Results show that in the near future (2020–2049) a small to null increase in heat stress may occur. In the far future (2070–2099), the frequency of heat stress during grain filling should increase significantly. Adaptation through earlier sowing dates proves to be the least efficient. Use of earlier heading cultivars is somewhat efficient, and should be sufficient for the near future. Tolerance to heat stress appears to be the most promising adaptation strategy. We discuss the importance of placing earliness and heat tolerance high on the agenda of wheat research and breeding, and the potential use of modelling in evaluating such strategies.